{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T18:36:45Z","timestamp":1778611005908,"version":"3.51.4"},"reference-count":18,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2019,2,1]],"date-time":"2019-02-01T00:00:00Z","timestamp":1548979200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11701171, 11771454"],"award-info":[{"award-number":["11701171, 11771454"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the Scientific Research Fund of Hunan Provincial Education Department of China","award":["17B113"],"award-info":[{"award-number":["17B113"]}]},{"name":"the Hunan Provincial Natural Science Foundation of China","award":["2016JJ4037"],"award-info":[{"award-number":["2016JJ4037"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we present two kinds of Hermite-type collocation methods for linear Volterra integral equations of the second kind with highly oscillatory Bessel kernels. One method is direct Hermite collocation method, which used direct two-points Hermite interpolation in the whole interval. The other one is piecewise Hermite collocation method, which used a two-points Hermite interpolation in each subinterval. These two methods can calculate the approximate value of function value and derivative value simultaneously. Both methods are constructed easily and implemented well by the fast computation of highly oscillatory integrals involving Bessel functions. Under some conditions, the asymptotic convergence order with respect to oscillatory factor of these two methods are established, which are higher than the existing results. Some numerical experiments are included to show efficiency of these two methods.<\/jats:p>","DOI":"10.3390\/sym11020168","type":"journal-article","created":{"date-parts":[[2019,2,1]],"date-time":"2019-02-01T11:19:58Z","timestamp":1549019998000},"page":"168","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Hermite-Type Collocation Methods to Solve Volterra Integral Equations with Highly Oscillatory Bessel Kernels"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3662-538X","authenticated-orcid":false,"given":"Chunhua","family":"Fang","sequence":"first","affiliation":[{"name":"College of Mathematics, Hunan Institute of Science and Technology, Yueyang 414006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guo","family":"He","sequence":"additional","affiliation":[{"name":"College of Economics, Jinan University, Guangzhou 510632, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuhuang","family":"Xiang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Central South University, Changsha 410083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,2,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1137\/S1064827503428539","article-title":"A fast algorithm for the electromagnetic scattering from a large cavity","volume":"27","author":"Bao","year":"2005","journal-title":"SIAM J. 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